A dynamic approach to the tendency of industries to cluster

This can be written as:
(12) Z = x_n1 Ph P ^{- -}

1

( ⁿ1             ⁿ2               A 1-n

^, wh^{ere p} = I ∑ p}1 ^{σ +}∑⁽p_j21^)1-σ I

V i =1            i =1                )

producer service varieties enter the sub-production function of the manufacturing firm,
this expression of P can be simplified to read:
^{(13) p} = (n 1 p 1^{-σ +} n2⁽ p21^)1-σ )^1-σ

, which the same as Equation (2). To see that P is the cost function, we solve for input
demand:
(14) x_fl1 = ZPi-^σ P p

Letting the cost function be evaluated at a production of Z=1 leads to:

√^-σ

(¹⁵) c = ∑ P11^-σP^σ +∑ (Pi21)^1-σ P^σ = P^{σ (}n 1 p1^-σ + n2(P21)^{1-σ )1}-σ = P^σP¹-^σ = P

i                                         i

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